Question

Match the derivatives from the table (drawn inside)

with the points a,b,c,d,e from the graph attached inside.

please explain!thanks!

Answer 1

graph!

Answer 2

the derivative is how sloped the curve is,
when the curve is going down, the derivative isn negative,
when the curve is flat, the derivative is zero,
and when the curve is going up, the derivative is positive

Answer 3

f'(x) x
0 d
0.5 b
2 c
-0.5 a
-2 e

the derivative represents the slope of the function at any point.
the one with slope=0 represents a horizontal tangent line at d.
the steeper tangent line has a greater value
a positive value makes a tangent line that passes through the first and third quadrants
a negative value makes a tangent line that passes through the second and fourth quadrants.

Answer 4

the steeper the curve the more positive or negative its derivative is

Answer 5

ohhh okay, @UnkleRhaukus i will try to remember that:)

and @ali_rami1990 so you determined all that based off which quadrants they were in and such?

Answer 6

well, I wrote that for you to differentiate between negative and positive slopes, can you?,
if yes, then no need to read about it..

Answer 7

haha okay:)

yeah it makes sense now:)

and since i can see the visuals and compare, i think i understand it:)

thank you!!!

Answer 8

You're welcome :)